As an initial motivation, let us give a rough argument to introduce para-Hermitian
and generalized geometry in string theory, and their connections with T-duality.
When considering string toroidal compactifications, a distinctive feature of strings is that their extended
nature allows them to wrap non-contractible cycles around the compact dimensions.
As a consequence, strings are not only characterized by momentum modes but also by
winding modes, which describe how the strings wind around the tori.
Roughly speaking, T-duality is a symmetry of string theory that establishes that momentum and winding states should
be considered on an equal footing.
As a simple example, suppose we have only one compact dimension, a circle \(S^{1}\)  with radius \(R\) .
The momentum and winding modes are quantized; they are characterized by two quantum numbers \(n,m\) .
From the mass spectrum for closed strings one can see (as a standard reference cf. [1]})
that, when \(R\rightarrow \infty \) , winding modes become very heavy, while momentum
modes become light and start to form a continuum, as corresponds to a non-compact dimension.
Similarly, when \(R\rightarrow 0\) , momentum modes become infinitely massive
but winding modes become light, and the spectrum again approaches a continuum.
Therefore, the \(R\rightarrow \infty \)  and \(R\rightarrow 0\)  limits appear to be physically equivalent, a remarkable feature that is exclusive
to string theory since a field theory of point-like particles has no winding states (so no spacetime dimension
`opens up' when \(R\rightarrow 0\)  in that case).
This equivalence comes from the fact that the string spectrum is invariant under the simultaneous change
\(R \leftrightarrow \alpha ^{\prime }/R\) , \(n \leftrightarrow m\)  (where \(\alpha ^{\prime }\)  is the inverse of the string tension), a symmetry which
extends to any observable in the theory.
This is the simplest manifestation of T-duality;
more generally, T-duality relates the physics of strings propagating on backgrounds with very different geometries.
